It may ask you for a username and password, this will be your departmental account. The username should be prefixed with "DEPT\" (again excluding quotation marks.) If your password is rejected, it's possible that you need to change it or it has expired. The easiest way to test this is to go to the library and log in on one of the PCs there.
Once authenticated you should then see the list of printers, and right click the printer of interest and choose "Connect...".
Depending on your version of windows you may have to reconnect to the print server every time you restart, it might be a good idea to create a shortcut.
The copier is a special case where print jobs sent are not printed at either copier until a PIN is entered. When the PIN is entered you can choose queued jobs to print to the copier you are using. Here is a video.